scholarly journals Regularization of the Divergent Integrals. I. General Consideration.

2007 ◽  
Vol 4 (2) ◽  
Author(s):  
Vladimir Zozulya
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
General Consideration ◽  
Science And Engineering ◽  
Hypersingular Integrals ◽  
Weakly Singular ◽  
Easy Calculation ◽  
Multidimensional Integrals

This article considers weakly singular, singular and hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used to solve problems in science and engineering. For their regularization, an approach based on the theory of distribution and application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular and hypersingular integrals, have been constructed. Such approach may be easily generalized and applied to the calculation of multidimensional integrals with singularities of various types.

scholarly journals The Regularization of the Divergent Integrals in 2-D Elastostatics

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
V. V. Zozulya
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Elements ◽  
Boundary Integral ◽  
Hypersingular Integrals ◽  
Green's Theorem ◽  
Curved Boundary ◽  
Green’S Theorem ◽  
Weakly Singular ◽  
Easy Calculation

This article considers weakly singular, singular and hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used to solve problems in 2-D elastostatics. For their regularization, an approach based on the theory of distribution and application of the Green’s theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular and hypersingular integrals for straight and curved boundary elements, have been constructed.

scholarly journals Divergent Integrals in Elastostatics: General Considerations

2011 ◽  
Vol 2011 ◽  
pp. 1-25 ◽  
Author(s):  
V. V. Zozulya
Keyword(s):  
Integral Equation ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Boundary Element Methods ◽  
Hypersingular Integrals ◽  
Integral Equation Methods ◽  
Weakly Singular ◽  
Easy Calculation ◽  
2D And 3D

This article considers weakly singular, singular, and hypersingular integrals, which arise when the boundary integral equation methods are used to solve problems in elastostatics. The main equations related to formulation of the boundary integral equation and the boundary element methods in 2D and 3D elastostatics are discussed in details. For their regularization, an approach based on the theory of distribution and the application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular, and hypersingular integrals, have been constructed.

scholarly journals Symmetric Complex Boundary Element Scheme for 2-D Stokes Mixed Boundary Value Problem

2016 ◽  
Vol 13 (1) ◽  
Author(s):  
Sun-Gwon Hong
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Boundary Integral ◽  
Hypersingular Integrals ◽  
Element Scheme ◽  
Boundary Limit ◽  
Complex Boundary ◽  
Gt Element

For 2-D Stokes mixed boundary value problems we construct a boundary<br />integral equation which couples a conventional boundary integral equation<br />for the velocity with a hypersingular boundary integral equation for the<br />traction. Expressing terms in the equation by complex variables, we obtain a<br />complex boundary integral equation and realize symmetrization of boundary<br />element scheme by Galerkin method. Applying a boundary limit method, we<br />obtain exact calculation formulae for calculation of hypersingular boundary<br />integrals. It is shown that all divergent terms in hypersingular integrals<br />cancel each other out.

scholarly journals Integral and differential equations for conformal mapping of bounded multiply connected regions onto a disk with circular slits

2014 ◽  
Vol 7 (1) ◽  
Author(s):  
Ali H.M. Murid ◽  
Ali W. Kareem Sangawi ◽  
M.M.S. Nasser
Keyword(s):  
Integral Equation ◽  
Conformal Mapping ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Science And Engineering ◽  
Multiply Connected ◽  
Circular Slit ◽  
Multiply Connected Regions ◽  
Multiply Connected Region ◽  
Neumann Kernel

Conformal mapping is a useful tool in science and engineering. On the other hand exact mapping functions are unknown except for some special regions.In this paper we present a new boundary integral equation with classical Neumann kernel associated to f f , where f is a conformal mapping ofbounded multiply connected regions onto a disk with circular slit domain. This boundary integral equation is constructed from a boundary relationshipsatisfied by a function analytic on a multiply connected region. With f f known, one can then treat it as a differential equation for computing f .

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